3D Computer Vision Omnidirectional VisionOmnidirectional Vision

Lecture 3 - Part 2Omnidirectional Cameras

Spring 2006

Zhang Aiwu

3D Computer Vision Lecture OutlineLecture Outline Applications

Robot navigation, Surveillance, Smart rooms Video-conferencing/ Tele-presence Multimedia/Visualization GIS

Page of Omnidirectional Vision (Many universities and companies….) http://www.cis.upenn.edu/~kostas/omni.html

Design Requirements 360 degree FOV, or semi-sphere or full sphere in one snapshot Single effective viewpoint Image Resolutions – one or more cameras? Image Sharpness – optics as well as geometry

Several Important Designs Catadioptric imaging : mirror (reflection) + lens ( refraction) Mirrors: Planar, Conic, Spherical, Hyperboloidal, Ellipsoidal, Paraboloidal Systematic design ( S. Nayar’s group)

Calibrations Harder or simpler?

3D Computer Vision

From the Page of Omnidirectional Vision http://www.cis.upenn.edu/~kostas/omni.html

From the Page of Omnidirectional Vision http://www.cis.upenn.edu/~kostas/omni.html

Which one?Which one?Which one?Which one?Which one?

3D Computer Vision (Poly-)Dioptric solutions(Poly-)Dioptric solutions

Homebrewed polydioptric cameras are cheaper, but require calibrating and synchronizing;

commercial designs tend to be expensive

One to two fish-eye cameras or many synchornized cameras

3D Computer Vision Catadioptric solutionsCatadioptric solutionsUsually single camera combined with convex mirror

Cons:- Blindspot- Low resolution

Pros: - Single image

3D Computer Vision Sensor DesignSensor Design Catadioptric imaging :

mirror (reflection) + lens ( refraction) Theory of Catadioptric Image Formation ( S. Nayar’s group)

"A Theory of Single-Viewpoint Catadioptric Image Formation" , Simon Baker and Shree K. Nayar ,International Journal of Computer Vision, 1999.

Mirrors Planar Conic, Spherical Hyperboloidal, Ellipsoidal Paraboloidal

Cameras (Lens) Perspective (pinhole) or orthogonal (tele-centric lens) projection One or more?

Implementations Compactness - size, support, and installation Optics – Image sharpness, reflection, etc.

3D Computer Vision Planar MirrorPlanar Mirror

Panoramic camera system using a pyramid with four (or more) planar mirrors and four (or more) cameras (Nalwa96) has a single effective viewpoint

4 camera design and 6 camera prototype:

FullView - Lucent Technology http://www.fullview.com/

6 cameras

Mirror pyramid

3D Computer Vision Planar MirrorPlanar Mirror

Panoramic camera system using a pyramid with four (or more) planar mirrors and four (or more) cameras (Nalwa96) has a single effective viewpoint

P1

P2

Viewpoint of the Virtual camera

Geometry of 4 camera approach: four separate cameras in 4 viewpoints can generate images with a single effective viewpoint

3D Computer Vision Planar Mirror ApproachPlanar Mirror Approach

A single effective viewpoint More than one cameras High image resolution

3D Computer Vision Planar Mirror ApproachPlanar Mirror Approach

A single effective viewpoint More than one cameras High image resolution

3D Computer Vision Conic MirrorConic Mirror Viewpoints on a circle semispherical view except occlusion Perspective projection in each direction Robot Navigation (Yagi90, Zhu96/98)

viewpoint

pinhole

3D Computer Vision Spherical MirrorSpherical Mirror

Viewpoints on a spherical-like surface Easy to construct (Hong91 -UMass )

Intersection of incoming rays are along this lineLocus of

viewpoints

3D Computer Vision Hyperboloidal MirrorHyperboloidal Mirror Single Viewpoint

if the pinhole of the real camera and the virtual viewpoint are located at the two loci of the hyperboloid

Semi-spherical view except the self occlusion

pinhole

P1

viewpoint

P2

Rotation of the hyperbolic curve generates a hyperboloid

3D Computer Vision Hyperboloidal MirrorHyperboloidal Mirror ACCOWLE Co., LTD, A Spin-off at Kyoto University

http://www.accowle.com/english/  Spherical Mirror Hyperbolic Mirror

Image: High res. in the top

3D Computer Vision Ellipsoidal MirrorEllipsoidal Mirror Single Viewpoint

if the pinhole of the real camera and the virtual viewpoint are located at the two loci of the ellipsoid

Semi-spherical view except the self occlusion

pinhole

viewpoint

P1

P2

3D Computer Vision Panoramic Annular Lens

panoramic annular lens (PAL)- invented by Pal Greguss* 40 mm in diameter, C-mount* view: H: 360, V: -15 ~ +20* single view point (O)

- geometric mathematical model for image transform & calibration

p p1

pinhole

P1

P

B

O

C

Ellipsoidal mirror

Hyperboloidal mirror

3D Computer Vision Panoramic Annular Lens

panoramic annular lens (PAL)- invented by P. Greguss* 40 mm in diameter, C-mount* view: H: 360, V: -15 ~ +20•single view point (O)•C-Mount to CCD Cameras

Image: High res. In the bottom

3D Computer Vision Cylindrical panoramic un-warping

Circular to cylindrical transformationafter eliminating radial distortion

Two Steps:

(1). Center determination

(2) Distortion rectification

2-order polynomial approximation

3D Computer Vision Paraboloidal MirrorParaboloidal Mirror

Semi-spherical view except the self occlusion Single Viewpoint at the locus of the paraboloid, if

Tele-lens - orthographic projection is used Mapping between image, mirror and the world invariant to

translation of the mirror. This greatly simplifies calibration and the computation of perspective images from paraboloidal images

P1

viewpoint

tele-lens

P2

3D Computer Vision Paraboloidal MirrorParaboloidal Mirror

Remote Reality – A Spin-off at Columbia University

http://www.remotereality.com/

Camcorder Web Camera Back to Back : Full Spherical View

3D Computer Vision Paraboloidal MirrorParaboloidal Mirror

Remote Reality – A Spin-off at Columbia University

http://www.remotereality.com/

3D Computer Vision

Q: What kind of sensor should one use?

A: Depends on your application.

1. If you are primarily concerned with:– resolution – surveillance (coverage)

and can afford the bandwidth & expense,you might stick with polydioptric solutions

2. If you are concerned with– bandwidth –servoing, SFM

investigate catadioptric or single wideFOV dioptric solutions

Confused?Confused?Confused?Confused?Confused?Confused?Confused?

3D Computer Vision ApplicationApplication

3D Computer Vision ApplicationApplication

3D Computer Vision ApplicationApplication

3D Computer Vision ApplicationApplication

3D Computer Vision ApplicationApplication

3D Computer Vision

城市的街道和建筑物日新月异，使得汽车导航系统必须不断更新地图。日本的一种新技术利用全球卫星定位系统（ GPS ）和360 度全景照相机，可以及时发现城市变化，并修改地图。

据《日经产业新闻》日前报道，这种技术由日本名古屋大学教授村濑洋的研究小组开发，能够将 GPS 提供的位置信息和来自全景照相机的图像信息组合起来，自动检索出建筑物所处位置。

这项技术首先利用搭载有全景照相机的公交和出租车收集图像。这些车辆一边穿街走巷一边拍摄周围的情况，然后将拍摄到的图像汇总到计算机。根据车上 GPS 提供的位置信息，就可以迅速判断出所收集到的图像是在何时、何地拍摄的。

     GPS 的位置信息存在 10 米左右的误差，但是计算机能够通过比对多辆汽车传来的图像进行自动调整，从而将误差控制在 40 厘米以内。应用这种图像识别技术，就可以在街道情况出现变化时迅速更新城市地图。

用 GPS 和全景相机 日本开发出绘城市地图新技术

3D Computer VisionImage Properties of Paraboloid System Image Properties of Paraboloid System

The Image of a Line is a circular arc if the line is not parallel to the optical axis Is projected on a (radial) line otherwise

Dual Vanishing Points There are two VPs for each set of parallel lines, which are

the intersections of the corresponding circles Collinear Centers

The center of the circles for a set of parallel lines are collinear

Vanishing Circle The vanishing points of lines with coplanar directions* lie

on a circle ( all the lines parallel to a common plane)

(Assuming aspect ratio = 1)

3D Computer VisionImage Properties of Paraboloid System Image Properties of Paraboloid System

The Image Center Is on the (“vanishing”) line connecting the dual vanishing

points of each set of parallel lines Can be determined by two sets of parallel lines

Projection of a Line with unknown aspect ratio Is an elliptical arc in the general case

The Aspect Ratio Is determined by the ratio of the lone-short axes of the

ellipse corresponding to a line Intrinsic Calibration

Estimate aspect ratio by the ratio of ellipse Estimate the image center by the intersection of vanishing

lines of two sets of parallel lines in 3-D space

(with aspect ratio)

3D Computer Vision Calibration of Paraboloid System Calibration of Paraboloid System

The Image Center Is on the (“vanishing”) line connecting the dual vanishing

points of each set of parallel lines Can be determined by two sets of parallel lines

3D Computer Vision Calibration of Paraboloid System Calibration of Paraboloid System

The Image Center Yellow “vanishing” line of horizontal set of parallel lines Pink “vanishing” line of vertical set of parallel lines

The Vanishing Circle (Red dotted) The vanishing points of lines with coplanar directions ( on a plane in this example)

Projected to the plane of the calibration pattern

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